Given a $n \times n$ matrix, the $(i, j)$ minor is the determinant of the submatrix formed by deleting the i-th row and j-th column. If the sum of all row vectors and the sum of all column vectors are both 0, then the $(i, j)$ minor does not depend on the choice of $i$ and $j$ (up to $\pm 1$). In knot theory, this is used to define the determinate of a knot via coloring matrix.
My question is, can we find a necessary and sufficient condition for the matrix such that the absolute values of all $(n-1)\times (n-1)$ minors of it are equal? Or some other sufficient conditions besides the above one?
